Suppose that P is a critical point of z = f (x, y). Suppose further that at P, the following hold: a² f əx² a² f Əy² -3, -2, 8² f a² f əyəx dady What can we say about point P? ▼ƒ(P) ‡ 0 -1. The function has a local minimum at P The function has a local maximum at P The function has a saddle point at P

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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Suppose that P is a critical point of z = f (x, y).
Suppose further that at P, the following hold:
a² f
მ2
a² f
dy²
–3,
-2,
8² f
a² f
əyəx
მე მყ
What can we say about point P?
○ Vƒ(P) 0
−1.
The function has a local minimum at P
The function has a local maximum at P
The function has a saddle point at P
Transcribed Image Text:Suppose that P is a critical point of z = f (x, y). Suppose further that at P, the following hold: a² f მ2 a² f dy² –3, -2, 8² f a² f əyəx მე მყ What can we say about point P? ○ Vƒ(P) 0 −1. The function has a local minimum at P The function has a local maximum at P The function has a saddle point at P
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